Tension softening of quasi-brittle materials modelled by singly and doubly periodic arrays of coplanar penny-shaped cracks

Abstract

The tension softening response of quasi-brittle materials such as concrete, rocks and most ceramics is described by modelling the localized deformation along the eventual fracture plane with singly and doubly periodic arrays of penny-shaped cracks. Mathematically, the study requires the solution of an integral equation for a function of two independent variables. To improve the accuracy of the numerical solution procedure especially when the neighbouring cracks come close to, and eventually touch one another, the integral equation is reduced to one involving a function of a single independent variable. This reduction is based on a key assumption that is akin to the Saint Venant principle. It is believed that the approximate method of solution is highly accurate, although in the absence of an exact solution at present it is difficult conclusively to prove this belief.